We normally characterize the apparent brightness of a star by its

How can we express the intrinsic brightness of a star in terms of
magnitudes? One means is to imagine moving the star to a
predetermined distance. The **absolute magnitude** of a star,
M_{v}, is defined to be the apparent brightness of a star when
the star is at a distance of 10 pc (32.6 light years). The difference
between the apparent magnitude and absolute magnitude provides
(almost) enough information to calculate the distance to the star. If
you are interested, you can read more about apparent and absolute magnitudes.

In order to find the distance to M100, you need to find the absolute
magnitudes for each of the Cepheids. Henrietta Leavitt of the Harvard
College Observatory discovered the relationship between the period of
Cepheids and their average apparent magnitude m_{v}. She had
studied Cepheids in the Large and Small Magellanic Clouds, but did not
know the distance to the Cepheids, and therefore could not establish
absolute magnitudes or luminosities for the Cepheids. Harlow Shapley
determined the calibration needed to turn Leavitt's period - apparent
magnitude diagram (P-m_{v} relation) into a period-luminosity
relation (P-L relation) for Cepheids. Since the luminosity of a star
is related to its absolute visual magnitude (M_{v}), we can
express the P-L relationship as a P-M_{v} relationship. The
P-M_{v} relationship for M100 is shown graphically below:

The relationship is described by the equation (from Ferrarese *et
al.,* 1996)

where P is in days. If logarithms are a faint memory, you may wish to peruse a refresher on logs.

For each Cepheid you discovered, use the above equation to determine the absolute magnitude of the Cepheid from its period.

For example, in the demonstration of the Cepheid hunt, you found Cepheid C46. Part I, Section B of your lab sheet for this Cepheid looks like this:

Cepheid name Grid # Avg mFrom column 4, the period of the Cepheid is 25.3 days. Using the equation above, the average absolute magnitude of C46 is_{v}P(days) M_{v}m_{v}-M_{v}C46 47 25.3 25.3 ____________ ______ ______ _______ ______ ______ ____________ ______ ______ _______ ______ ______

Enter the absolute magnitude in column 5 of Part I, Section B of your lab sheet. The entry for C46 now looks like:

Cepheid name Grid # Avg m_{v}P(days) M_{v}m_{v}-M_{v}C46 47 25.3 25.3 -5.27 ____________ ______ ______ _______ ______ ______ ____________ ______ ______ _______ ______ ______

Find the absolute magnitudes for all your Cepheids, and enter the result in column 5 of Part I, Section B of your lab sheet.

On to The distance to M100

Back to Find the Cepheids!

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